(Reuters) - Sprint Nextel Corp urged Clearwire Corp to reject Dish Network's rival bid for the wireless service provider, saying that a deal under Dish's terms would be illegal and violate Clearwire's agreement with its shareholders.

Sprint, which made its case in a letter to Clearwire's board on Monday, already owns a majority stake in Clearwire and is tussling with Dish to buy out minority shareholders.

Satellite TV provider Dish offered $4.40 per share for Clearwire on May 29, challenging Sprint's revised bid of $3.40 per share. The fight over Clearwire, which owns wireless airwaves that both suitors want, is part of a larger drama involving the fate of Sprint.

Dish has also made an offer to buy Sprint, the No. 3 U.S. wireless service provider, for $25.5 billion. Japan's SoftBank Corp already has an agreement to buy Sprint.

Sprint said many of Dish's conditions in its Clearwire offer are impossible to fulfill because approval is required from all shareholders including Sprint, which said it would not give up any of its rights with regards to Clearwire's governance.

Sprint said Dish's demand for the right to nominate three Clearwire board members runs roughshod over Clearwire's equity holder agreement, which includes a director selection process.

It also said that granting several of Dish's demands would violate Delaware law as well as Clearwire's existing agreements.

"Many Clearwire stockholders appear to be under the mistaken belief that Dish's proposal is a viable alternative to the Sprint merger agreement, and this is simply not the case." Sprint said in its letter.

Clearwire has kept its recommendation to shareholders for the Sprint offer while its special committee reviews Dish's bid. Clearwire declined to comment on Sprint's Monday letter.

Clearwire shareholders are due to vote on the Sprint offer at a special meeting on June 13 in which Sprint would need more than 50 percent of minority votes for its deal to succeed.

On top of its battle with Dish, Sprint also faces trouble from powerful activist shareholders. Four shareholders claiming 18.2 percent of the minority shares extended a pledge to work together until after the vote to try to get a better deal.

The group led by investment firm Mount Kellett believes the Dish offer "is both actionable and obviously superior," according to a regulatory filing by Mount Kellett.

Another big investor, Crest Financial, which holds about 8 percent of Clearwire's public shares, blasted Sprint on Monday, demanding that Clearwire give full consideration to Dish's bid. Crest has been running a proxy battle against Sprint's offer.

Sprint had originally agreed to buy Clearwire in December for $2.97 per share but it increased its offer to $3.40 per share on May 21 under pressure from shareholders.

Pacific Crest analyst Michael Bowen questioned why Sprint raised its bid, given its position as majority shareholder. He worried that "this may end up in court and delay Sprint's ability to put this transaction behind them."

Sprint shareholders are due to vote June 12 on SoftBank's offer to buy 70 percent of the company for $20.1 billion.

Dish did not provide a comment on Sprint's letter.

On Nasdaq, Clearwire closed off 1.3 percent at $4.42, and Dish was down 10 cents at $38.64. Sprint dipped 8 cents to $7.22 on the New York Stock Exchange.

(Additional reporting by Jennifer Saba in New York and Sayantani Ghosh in Bangalore; Editing by Saumyadeb Chakrabarty, Lisa Von Ahn, John Wallace and Richard Chang)